Related papers: A Semidefinite Programming-Based Branch-and-Cut Al…

This paper presents a co-clustering technique that, given a collection of images and their hierarchies, clusters nodes from these hierarchies to obtain a coherent multiresolution representation of the image collection. We formalize the…

Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…

Graph clustering is a challenging pattern recognition problem whose goal is to identify vertex partitions with high intra-group connectivity. This paper investigates a bi-objective problem that maximizes the number of intra-cluster edges of…

The goal of co-clustering is to simultaneously identify a clustering of rows as well as columns of a two dimensional data matrix. A number of co-clustering techniques have been proposed including information-theoretic co-clustering and the…

When solving numerical constraints such as nonlinear equations and inequalities, solvers often exploit pruning techniques, which remove redundant value combinations from the domains of variables, at pruning steps. To find the complete…

Biclustering is a powerful approach to search for patterns in data, as it can be driven by a function that measures the quality of diverse types of patterns of interest. However, due to its computational complexity, the exploration of the…

Maximal biclique enumeration is a fundamental problem in bipartite graph data analysis. Existing biclique enumeration methods mainly focus on non-attributed bipartite graphs and also ignore the \emph{fairness} of graph attributes. In this…

Identifying a biclique with the maximum number of edges bears considerable implications for numerous fields of application, such as detecting anomalies in E-commerce transactions, discerning protein-protein interactions in biology, and…

How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…

We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…

We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear…

Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…

In the presence of heterogeneous data, where randomly rotated objects fall into multiple underlying categories, it is challenging to simultaneously classify them into clusters and synchronize them based on pairwise relations. This gives…

It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…

Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…

Many datasets take the form of a bipartite graph where two types of nodes are connected by relationships, like the movies watched by a user or the tags associated with a file. The partitioning of the bipartite graph could be used to fasten…

Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques…

Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…